A 52nd-minute goal by Edin Dzeko levelled the aggregate score at 2-2, which, combined with Cengiz Under's crucial first-leg goal at the Metalist Stadium in Kharkiv, proved enough to see the Italian outfit through on the away-goal rule.
A 79th-minute red card to Ivan Ordets all but scuppered any attempt at a comeback for Shakhtar, as Roma saw out the result before celebrating in front of a raucous home crowd. Not that the Romans were tested much over 90 minutes; Shakhtar failed to record a single shot on target, even though the Ukrainian outfit maintained 59 percent possession.
Roma's round of 16 triumph sees the club advance to the final eight of the tournament for the first time since the 2007-08 season, the year that the Italian outfit defeated Real Madrid 2-1 in both legs before losing to Manchester United in the next round.
The 1-0 scoreline also sees Roma preserve its perfect goals-against record at the Stadio Olimpico in Champions League play this season, having previously recorded a 0-0 draw with Atletico Madrid, a 3-0 win over Chelsea, and a 1-0 win over Qarabag in the group stage of the competition.